Optimal mean firstpassage time for a Brownian searcher subjected to resetting: Experimental and theoretical results
Abstract
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the resetting position are Gaussian distributed with width σ . We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full firstpassage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean firstpassage time as a function of the resetting period and rate for different values of the ratio b =L /σ and find an interesting phase transition at a critical value b =b_{c} . For b_{c}<b <∞ , there is a metastable optimum time which disappears for b <b_{c} . The intrinsic difficulties in implementing these protocols in experiments are also discussed.
 Publication:

Physical Review Research
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevResearch.2.032029
 arXiv:
 arXiv:2004.11311
 Bibcode:
 2020PhRvR...2c2029B
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 Phys. Rev. Research 2, 032029 (2020)